Study of Wear of Pitched Blade Impellers in a Solid-Liquid Suspension

A study was made of the erosion wear of the blades of pitched blade impellers in a suspension of silicious sand (C V = 5 %, d=0.325 mm, degree of hardness "7.5") in water under a turbulent flow regime of agitated charge when complete homogeneity of the suspension was achieved. Two aims of the study were defined: the dependence of the rate of the erosion process of the impeller blades on impeller frequency of revolution and on the size of the mixing equipment. Experiments were carried out on pilot plant mixing equipment of two sizes (geometrically similar) made of stainless steel (diameters of cylindrical vessels T 1 = 200 mm and T 2 = 300 mm, diameters of impellers D 1 = 100 mm and D 2 = 66. 7 mm, impeller off bottom clearances h 1 = 100 mm and h 2 = 66. 7 mm, respectively) equipped with four radial baffles (width b 1 = 30 mm, b 2 =20 mm, respectively) and an impeller with four inclined plane blades (pitch angle α =30°, 45°, relative blade with W/D = 0.2) made of rolled brass (Brinnel hardness 40-50 BM) always pumping the liquid downwards towards the float vessel bottom. The wear of the impeller was described by an analytical approximation in exponential form with two parameters (the wear rate constant k and the geometrical parameters of the worn blade C) calculated by the least squares method from the experimentally found profile of the worn leading edge of the impeller blades. While the wear rate constant exhibits a monotonous dependence on the pitch angle only, the geometric parameter is dependent both on the pitch angle and in linear form on the impeller tip speed. Thus in the procedure for scaling up the rate of erosion wear of the pitched blade impellers in a suspension of higher solid particle hardness, the decision process parameters are the impeller blade pitch angle and the impeller tip speed.


Introduction
The erosion proeess of a pitehed blade impeller in a solid liquid suspension of particles higher hardness was reeently studied [1,2,3,4], and a simplified two parameter model of the proeess was proposed and experimentally verified.The wear ofthe impeller ean be deseribed by an analytieal approximation in exponential formo lt follows from the above mentioned investigations that the wear rate constant does not depend on time, but that it signifieantly depends on the piteh angle.However, the geometrie parameter depends both on the duration of the erosion period and on the blade piteh angle.
The veloeity of two-phase flow affeets the erosion proeess of a fiat plate or impeller blade loeated in the stream of a solid-liquid suspension [5,6].Moreover, when sealing up the mixing equipment it is desirable to take into eonsideration eertain requirements of the proeedure, beeause even when there is geometrie similarity between the pilot plant and the industrial mixing unit it is neeessary to fulfill suitable sealing up rules when using the results from pilot plant equipment experiments to design equipment on an industrial scale [7].
This study attempts to extend our knowledge about the meehanism of erosion wear of the blades ofaxial impellers in a solid-liquid suspension to determine the influenee of the velocity of the two-phase flow around the blade, i.e. the impeller frequency of revolution, and to study the proeess in different sizes of mixing equipment, i.e. to look for the sealing up rules of the proeess.

Experimental
Experiments were earried out on pilot plant mlxmg equipment (see Fíg. I) oftwo geometrieally similar sizes: I. Larger unit: vessel diameterT I = 300 mm, height ofliquid from bottom ofvessel HI = 300 mm, diameter of impeller DI =100 mm., dynamie viseosity ~= I mPa•s) was used as the working liquid and silieious sand (volumetrie coneentration C v = 5 %, mean diameter of particles (median) d = 0.325 mm, density Ps = 2600 kg/m 3 , degree of hardness "7.5") was used as solid particles.Pitched blade impellers with four adjustable inclined plane blades (see Fíg. 2) made of rolled brass were used for the erosion tests, As independent variables we took the size ofthe mixing Fig. 2: Design of a pitched blade impeller with four inclined plane adjustable blades (Dr = 100 mm, Do, = 25 mm, Wr = 20 mm, sl = 1.2 t 0.04 mm; Dr = 66.7 mm, Do: = 20 mm, Wz= 13.3 mm, s2=0.8+0.04 mm; o=30',45') equipment (see above) and the frequency of the impeller revolution n, at two levels of pitch angle cr.In all cases the fre- quency of the impeller revolution was kept under conditions of complete homogeneity of suspension when a turbulent regime of flow of the agitated batch took place.For the experiments we used cylindrical metal bafiled vessels made of stainless steel (see lig. l).We used directly controlled alternat- ing current electric drives of impellers with simultaneous miasurement and control of the impeller frequency of revolu- tions within an accuracy t 1 Va from the set uP value.For the larger pilot plant unit, three levels of frequency were chosen ,r = SOb, 700, 900 RPM and for smaller one tlvo frequencies nz =700,900 RPM.
During the experiments the shape of the blade profile was determined fiom magnified copies of the worn impeller blades copied via a scanner to the PC (magnification ratio 2: l).The average course of the blade profile for the given length of the erosion Process was determined as an average curve from four individual worn impeller blades.
The investigation of the shape of the worn blade was com- pleted by determining its weight.All four blades were weighed on a scale with an accuracy + 5 mg and an average decrease of the blade Arz from the weight of the unworn blade mowascalculated at the given time period of the erosion process.In this way, the dependence of the quantity Ntt/wo on time was obtained.

Results and discussion
Four series of experiments were evaluated: an investiga- tion of pitched blade impellers with pitch angle cr' = 30" for both the larger and the smaller pilot plant systems and also pitched blade impellers with pitch angle a=45", again, for the larger and smaller pilot plant systems '  During the erosion process of the pitched blade impeller caused by solid particles of silicious sand, its metal plane blades change shape mainly around the leading edge The radial profile of the worn blade can be considered in dimensionless exponential form (see Frg. 3) where the dimensionless axial (vertical) coordinate along the width of the blade is H =z(x)lw (2) k = - 6.587   and the dimensionless longitudinal (radial) coordinate along the radius of the blade is X =2xlDX: 2x/D. ( The value of the parameters of Eq. (l)the wear rate constant A and the geometric parameter of the worn blade Cwere calculated by the least squares method from the experimentally found profile of the worn blade; each curve was calculated from 14 -16 points (X, H) with a regression coef- frcient better than R = 0.970.
Egs. 4 -7 illustrate examples of the dependence of the wear rate constant.A on the duration ofthe erosion process ' for the given size of impeller (pilot plant equipment) D, or D, and impeller pitch angle cr.The figrrres show that after an initial period, when parameterfr depends on time, the main part of this dependence exhibits a constant value of the parameter independent of time.Such independence corresponds to the modil idea [3] that the wear rate constant cannot be a func- tion of time.Nevertheless, the blade erosion mechanism at the beginning of the process cannot be described by meals of the co.tstantrate of erosion, although the calculated value A frts the experimental data in this part of the erosion process very well.As was found recently [3,4] significantly on the pitch angle: the lower the pitch angle, the higher the rate of the erosion process for aH investigated conditions in the pilot plant equipment.Table 1 summarizes the value of parameter k. lt fol1ows from the Table that for the given blade piteh angle the wear rate eonstant is independent of both the impeller revolution frequency and the size of the mixing equipment.Thus it seems to be a universal parameter dependent only on impeller design.--~-----r---..------  L-n= 500 RPM, l-n=700 RpM, a -z=900 RpM) impeller speed.Generally, the lower the blade pitch angle and the higher the frequency of revolurion of the impeller; ile higher the dependence of quantity Lm,hnoon time.A -n =500 RPM,I -n=700 RPM, a -z=900 RpM)

Conclusions
The rate of the erosion process of the pitched blade impeller in a solid-liquid suspension of a high degree ofhardness of its solid particles can be described by a universal kinetic equation with two parameters.The erosion rate con- stant is independent both of the size and of the frequency of revolution of the pitched blade impelle4 and the second parameter (the geometric parameter of the profile of the worn blade) depends on rhe impeller tip speed.

Fig. 3 :
Fig. 3: Radial profile of the leading edge of the worn blade of pitched blade impeller

Fig. 12 :
Fig. 12: Dependence of the average relative decrease of the weight of the worn blade on time (T, = 300 mm, e = 30o,

Fig. 13 :
Fig. 13: Dependence of the average relative decrease of the weight of the worn blade on rime (?, = 300 mm, o.=4bo, the profile of a worn blade volumetric concentration, m3/m3 slope ofdependence (4), h-' impeller diameter, m hub diameter, m average diameter of solid parricles, m dimensionless axial coordinate of the profile of the worn blade height of liquid from bottom of the vessel, m h impeller c1earance, m wear rare constant weight of impeller blade, kg change in the weight of impeller wom blade, kg impeller frequency of revolution, S-I regression coefficient thickness of impeller blade, m vessel diameter, m time, h width of impeller blade, m dimensionless longitudinal coordinate the radius of impeller blade longitudina!(radia!) coordinate along the radius of impeller blade, m axial (vertical) coordinate along the width of the blade, m pitch angle of blade, o density, kg m• 3 dynamic viscosity, Pa•s [2] Fořt, 1., Ambros, F., Medek, j.: Study o[ Wear and Tear o[ Axial Flow ImpeUers.Proceedings of the Fluid Mixing VI Conference (Editor: H. Benkreira), Bradford (England) 1999, p. 59-68.
Dependence of the worn blade geometric paramerer on the duration of the erosion process (Tr = 200 mm, a=45",n =500 RPM) remains constanr, i.e. the presented model is valid until the erosion process causes a reduction of the impeller diameter.The values of paramerer C depend on the piich angle of the blades: the lower the pitch angle, the higher the slope c of the linear dependence Tllble 2 summarizes all values of paramerer r in Eq. (4) at various investigated conditions for borh sizes of thi pilot plant mixing equipment as well as ar various impellei fre- quencies of revolution z.Frnally we calculated the ratio of pa- rameter c and the impeller tip speed nDn.The values of this ratio are also written in Thble 2. The Thble shows that the value of the geometric parameter of the erosion process of the worn blade depends ar rhe given impeller pitch angle on the impeller tip speed.The results of our experiments show a lin- ear dependence between these two quantities.

Table 2 :
Dependence ofparameter c on the process parameters ofFigs.l2and l3 illustrate the time dependence of the rela- tive decrease of the average weight of the worn blade Nn/m,rat di{ferent pitch angles and frequencies of impeller revolurion for both sizes of the agitated sysrem.Here quantity mocharacterizes the weight of the unworn blade ar the very beginning ofthe erosion process.It is clear fiom all the figures that the quantity Nn/moincreases almosr linearly with time.It seems that with nrnning time after some interval the rate of blade weight reduction decreases, especially at the lowest level of